Partial Differential Equations I · Applied Physics And Applied Mathematics
Weekly problem sets, of widely varying difficulty. Some are only a few short problems, others take hours and hours of struggle. 1 Midterm: In my opinion quite difficult because you haven't yet had time to figure out a way to learn from the book. Grades were bimodally distributed; most people got either around 65 or a 100. 1 Final: A bit easier than the midterm because by the end of the class, you've learned to extract useful facts from the textbook. Very similar to the previous years' tests that you are given on courseworks.
a couple of homeworks and a few "take home" quizzes that are assigned randomly throughout the semester, 1 midterm (also was not scheduled until 2 weeks before) and final
NOTHING changes from semester to semester for the homework, find someone who'd enrolled in it, and you have the 12 problem sets all in your hand: Just try to read the handwritings of the previous TAs.
10 problem sets (20% of grade), 1 midterm (30%), and a final (50%). The problem sets were all very time consuming (at least for me) and took up to 15 hours to complete. They were a mixture of applying methods to solve PDEs and writing proofs. The problems can get very long and contain a lot of terms, so you need to be careful about keeping track of everything or you'll get to the end with a solution that doesn't make sense and pages to pour over looking for that pesky π you lost along the way. The midterm was challenging, but doable if you go in prepared. A lot of people did poorly on the midterm and the professor recommended they drop the class, because the material only gets more challenging and the final is much more difficult than the midterm. I'd recommend over-preparing for the midterm to score points as a buffer for the final later on. The final was close to impossible to finish if you answered each question fully and simplified the answer completely. However, you could score most of the points on each question by answering the hefty portion and leaving a messy unsimplified answer. The average on both exams was low (62.5 for midterm, 57 for final), but he scaled the average to a B.
This class basically exposes you to a few PDE's and a handful of methods for solving them. Sobel is a much, much better teacher than most higher math professors. However, that places him slightly below the average in clarity and teaching ability. You will not learn everything you need to know in lecture. To do well, you need to be able to interpret the (laughably unfriendly) textbook's explanations and cryptic homework questions. His office hours are lightly attended, though sometimes a few very lost souls monopolize his time with silly questions. Solutions to the homeworks and previous tests are on courseworks which is quite helpful for exam prep.
One of the worst professors I have had at Columbia. I did not think he was that bad until the end of the semester, when he decided that it would be a great idea to e-mail his students about a final review session 1 hour before the actual review session took place, making an assumption that a. students would be awake at 10am to read this e-mail, and b. students check their e-mail CONSTANTLY and will have read the e-mail. To top it all off, he refused to post the practice final online saying that it was our fault for not attending the review session. Overall, a very disorganized professor, and not particularly great at teaching either. Homeworks were assigned erratically so we would not know what week a homework would be due, so it was definitely difficult to plan ahead.
Guillaume Bal could be your nightmare if you were to come to Columbia as a international student: He's got an accent, doesn't speak loud enough, and the class is very, very crowded, which means even if everyone tries to keep quiet, the heat in the room can still easily put you asleep. Yet he does provide very detailed explanation and derivation if you can adapt to the way he conveys his ideas, and with the help of CVN, you might be able to review the materials online after the course, or at least we were able to do so last Fall.
Professor Quenneville-Belair is a nice guy and very intelligent, but be wary, he doesn't pull any punches with this class. The course moves quickly and builds on itself throughout, so you have to stay on top of the material. Everything is taught directly from the textbook though, which certainly helps, and the TAs were great. My biggest reservation with Professor Quenneville-Belair is his unwillingness to release solutions. He explained that at our level of mathematical sophistication we shouldn't need solutions released for the homeworks because we should be able to identify when we've done something wrong and correct it... Like what? How are we supposed to learn if nobody tells us what we're doing wrong? Granted, this was his first semester teaching this course here, so I'm sure he got plenty of feedback on this point and will hopefully take a different approach in future semesters. Overall I worked very hard in this course and learned a lot. Not for the faint of heart, but if you're up for it you'll come out the other side knowing a lot about PDEs.
Weekly problem sets which can sometimes be very tough and will probably require trips to the help room. Get a group together asap. Mathematica is useful for some really ugly symbolic matrices later in the class. Midterm is fair. Final was doable with a little bit of inspiration.
Good prof. The material in this class starts easy, but gets pretty difficult by the end (There's a big learning curve if this is your first introduction to Fourier Series / Transforms). Sobel does a good job conveying intuition and providing useful analogies to get a feel for what's going on. The physical motivations are sometimes overly lengthy (especially for someone with no interest in physics), but can be helpful in certain cases. I took and dropped other profs for this course (looking at you, Courdourier) before Sobel; the difference is huge. As a math major in the college, this is the first app math course I took, and I think I walked away with a very good understanding of the material. Recommended.